The $C^*$-algebra of the exponential function
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Abstract:
The complex exponential function $e^z$ is a local homeomorphism and therefore gives rise to an étale groupoid and a $C^*$-algebra. We show that this $C^*$-algebra is simple, purely infinite, stable and classifiable by K-theory, and has both K-theory groups isomorphic to $\mathbb Z$. The same methods show that the $C^*$-algebra of the anti-holomorphic function $\overline {e^z}$ is the stabilisation of the Cuntz-algebra $\mathcal O_3$.References
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Additional Information
- Klaus Thomsen
- Affiliation: Institut for matematiske fag, Ny Munkegade, 8000 Aarhus C, Denmark
- Email: matkt@imf.au.dk
- Received by editor(s): September 23, 2011
- Received by editor(s) in revised form: February 24, 2012
- Published electronically: September 12, 2013
- Communicated by: Marius Junge
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 142 (2014), 181-189
- MSC (2010): Primary 46L35, 46L80
- DOI: https://doi.org/10.1090/S0002-9939-2013-11716-8
- MathSciNet review: 3119193